Sketch any function with a domain of (-3, ∞) and a range of (-∞, 5)

Here is a sketch of a function with a domain of \((-3, \infty)\) and a range of \((-\infty, 5)\). The function starts at \(x = -3\) with a value just below 5 and decreases as it moves to the right, staying below the line \(y = 5\). 

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Here are five related questions:
1. What is an asymptote, and how does it apply to this function?
2. Can you define a specific equation for this function based on the graph?
3. How would the function change if the domain were extended to include \(x = -3\)?
4. What are some examples of real-world phenomena that could be modeled by such a function?
5. How would you determine the inverse of this function, if it exists?

**Tip:** When sketching functions, it's helpful to consider how the domain and range constraints impact the overall shape of the graph.

Explore how to sketch a function with a domain of (-3, ∞) and a range of (-∞, 5). Understand the behavior of the function starting just below 5 at x = -3 and decreasing to stay below y = 5. Learn more about functions and graphing concepts.

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